Excavator four-bar linkage length and angle offset determination using a laser distance meter

ABSTRACT

An excavator calibration framework comprises an excavator, a laser distance meter (LDM), and a laser reflector. The excavator comprises a chassis, linkage assembly (LA), sensor, implement, and an architecture controller. The LA comprises a boom, stick, and four-bar linkage (4BL) with the sensor on a 4BL dogbone linkage. The architecture controller is programmed to generate a mapping equation comprising linkage angle inputs (a measured dogbone angle θ DF   Measured , an estimated implement angle θ GH   Estimated ) and n unsolved 4BL linkage length and angle offset parameters. The controller is programmed to generate and solve a set of m mapping equations comprising the n unsolved parameters.

CROSS REFERENCE TO RELATED APPLICATIONS

The present disclosure is a continuation of and claims priority to U.S.patent application Ser. No. 15/385,126, filed Dec. 20, 2016, entitled“EXCAVATOR FOUR-BAR LINKAGE LENGTH AND ANGLE OFFSET DETERMINATION USINGA LASER DISTANCE METER,” the entirety of which is incorporated byreferenced herein.

BACKGROUND

The present disclosure relates to excavators which, for the purposes ofdefining and describing the scope of the present application, comprisean excavator boom and an excavator stick subject to swing and curl, andan excavating implement that is subject to swing and curl control withthe aid of the excavator boom and excavator stick, or other similarcomponents for executing swing and curl movement. For example, and notby way of limitation, many types of excavators comprise a hydraulicallyor pneumatically or electrically controlled excavating implement thatcan be manipulated by controlling the swing and curl functions of anexcavating linkage assembly of the excavator. Excavator technology is,for example, well represented by the disclosures of U.S. Pat. No.8,689,471, which is assigned to Caterpillar Trimble Control TechnologiesLLC and discloses methodology for sensor-based automatic control of anexcavator, US 2008/0047170, which is assigned to Caterpillar TrimbleControl Technologies LLC and discloses an excavator 3D laser system andradio positioning guidance system configured to guide a cutting edge ofan excavator bucket with high vertical accuracy, and US 2008/0000111,which is assigned to Caterpillar Trimble Control Technologies LLC anddiscloses methodology for an excavator control system to determine anorientation of an excavator sitting on a sloped site.

BRIEF SUMMARY

According to the subject matter of the present disclosure, an excavatorcalibration framework comprises an excavator, a laser distance meter(LDM), and a laser reflector. The excavator comprises a machine chassis,an excavating linkage assembly, an implement dynamic sensor, anexcavating implement, and an architecture controller. The excavatinglinkage assembly comprises an excavator boom, an excavator stick, and afour-bar linkage. The excavating implement and the excavator stick aremechanically coupled through the four-bar linkage comprising animplement linkage of length GH, a rear side linkage of length FH, adogbone linkage of length DF, and a front side linkage of length DG. Theimplement dynamic sensor is positioned on the dogbone linkage of thefour-bar linkage. The excavating implement is configured to curlrelative to the excavator stick to define a plurality of implement curlpositions. The LDM is configured to generate an LDM distance signalD_(LDM) indicative of a distance between the LDM and the laser reflectorand an angle of inclination signal θ_(INC) indicative of an anglebetween the LDM and the laser reflector. The laser reflector isconfigured to be disposed at a position corresponding to a calibrationnode on the excavating implement. The architecture controller isprogrammed to generate a mapping equation comprising linkage angleinputs, unsolved linkage length parameters, and unsolved angle offsetparameters. The linkage angle inputs comprise a measured dogbone angleθ_(DF) ^(Measured) and an estimated implement angle θ_(GH) ^(Estimated)at an implement curl position. The unsolved linkage length parameterscomprise the linkage lengths GH, FH, DF, and DG of the four-bar linkage.The unsolved angle offset parameters comprise an offset implement angleθ_(GH) ^(Bias) of the excavating implement. The architecture controlleris further programmed to, for successive implement curl positions,generate a set of m mapping equations, wherein the set of m mappingequations comprises n unsolved linkage length and unsolved angle offsetparameters, and the iterative process is repeated until m>n. Thearchitecture controller is further programmed to solve the generated setof m mapping equations comprising the n unsolved parameters to determinethe linkage lengths GH, FH, DF, and DG of the four-bar linkage and theoffset implement angle θ_(GH) ^(Bias) of the excavating implement, andoperate the excavator using the linkage lengths GH, FH, DF, and DG, andthe offset implement angle θ_(GH) ^(Bias).

According to the subject matter of the present disclosure, an excavatorcomprises a machine chassis, an excavating linkage assembly, animplement dynamic sensor, an excavating implement, and an architecturecontroller. The excavating linkage assembly comprises an excavator boom,an excavator stick, and a four-bar linkage. The excavating implement andthe excavator stick are mechanically coupled through the four-barlinkage comprising an implement linkage of length GH, a rear sidelinkage of length FH, a dogbone linkage of length DF, and a front sidelinkage of length DG. The implement dynamic sensor is positioned on thedogbone linkage of the four-bar linkage. The excavating implement isconfigured to curl relative to the excavator stick to define a pluralityof implement curl positions. The architecture controller is programmedto generate a measured dogbone angle θ_(DG) ^(Measured) of the dogbonelinkage from the implement dynamic sensor, and generate a mappingequation comprising linkage angle inputs, unsolved linkage lengthparameters, and unsolved angle offset parameters. The linkage angleinputs comprise the measured dogbone angle θ_(DF) ^(Measured) and anestimated implement angle θ_(GH) ^(Estimated) at an implement curlposition. The unsolved linkage length parameters comprise the linkagelengths GH, FH, DF, and DG of the four-bar linkage. The unsolved angleoffset parameters comprise an offset dogbone angle θ_(DF) ^(Bias) of thedogbone linkage, and an offset implement angle θ_(GH) ^(Bias) of theexcavating implement. The architecture controller is further programmedto, for successive implement curl positions, generate a set of m mappingequations, wherein the set of m mapping equations comprises n unsolvedlinkage length and unsolved angle offset parameters, and the iterativeprocess is repeated until m>n. The architecture controller is furtherprogrammed to solve the generated set of m mapping equations comprisingthe n unsolved parameters to determine the linkage lengths GH, FH, DF,and DG of the four-bar linkage, the offset dogbone angle θ_(DF) ^(Bias)of the dogbone linkage, and the offset implement angle θ_(GH) ^(Bias) ofthe excavating implement, and operate the excavator using the linkagelengths GH, FH, DF, and DG, the offset dogbone angle θ_(DF) ^(Bias), andthe offset implement angle θ_(GH) ^(Bias).

Although the concepts of the present disclosure are described hereinwith primary reference to the excavator illustrated in FIG. 1, it iscontemplated that the concepts will enjoy applicability to any type ofexcavator, regardless of its particular mechanical configuration. Forexample, and not by way of limitation, the concepts may enjoyapplicability to a backhoe loader including a backhoe linkage.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The following detailed description of specific embodiments of thepresent disclosure can be best understood when read in conjunction withthe following drawings, where like structure is indicated with likereference numerals and in which:

FIG. 1 is a side view of an excavator incorporating aspects of thepresent disclosure;

FIG. 2 is a perspective view of a dynamic sensor disposed on a linkageof the excavator of FIG. 1 and according to various concepts of thepresent disclosure;

FIG. 3 is a side elevation view of a linkage assembly of an excavatorcalibration framework including a laser distance meter (LDM) andimplement dimension points of an excavating implement of the excavatorof FIG. 1;

FIG. 4 is a side elevation view of a four-bar linkage assembly of theexcavator of FIG. 1, according to various concepts of the presentdisclosure;

FIG. 5 is another side elevation view of the four-bar linkage assemblyof FIG. 4, according to various concepts of the present disclosure; and

FIG. 6 is a flow chart of a process used to determine four-bar linkagedimensions and angle offsets of the excavator of FIG. 1.

DETAILED DESCRIPTION

The present disclosure relates to earthmoving machines and, moreparticularly, to earthmoving machines such as excavators includingcomponents subject to control. For example, and not by way oflimitation, many types of excavators typically have a hydraulicallycontrolled earthmoving implement that can be manipulated by a joystickor other means in an operator control station of the machine, and isalso subject to partially or fully automated control. The user of themachine may control the lift, tilt, angle, and pitch of the implement.In addition, one or more of these variables may also be subject topartially or fully automated control based on information sensed orreceived by an adaptive environmental sensor of the machine. In theembodiments described herein, an excavator calibration frameworkutilizes a laser distance meter to determine four-bar linkage lengths ofexcavator limb components and related angle offsets, such as an angleoffset of one or more sensors disposed on those respective linkages, asdescribed in greater detail further below. Such determined values may beutilized by an excavator control to operate the excavator.

Referring initially to FIG. 1, an excavator calibration frameworkcomprises an excavator 100, a laser distance meter (LDM) 124, and alaser reflector 130. The excavator 100 comprises a machine chassis 102,an excavating linkage assembly 104, an implement dynamic sensor 120, anexcavating implement 114, and control architecture 106. The excavatinglinkage assembly 104 comprises an excavator boom 108, an excavator stick110, and a four-bar linkage 112. The excavating implement 114 and theexcavator stick 110 are mechanically coupled through the four-barlinkage 112. In embodiments, the laser reflector 130 is on a pole orsecured directly to the excavating implement 114. The LDM 124 may be,for example, a Bosch GLM 100C LDM as made commercially available byRobert Bosch GmbH of Germany. A laser signal from the LDM 124, which isplaced on ground 126, may be transmitted in a direction of an arrow 132to the calibration node and an aligned laser reflector, such as, forexample, the laser reflector 130, and the laser signal may be reflectedback to the LDM 124 in the direction of an arrow 134, as illustrated inFIG. 1.

In embodiments, the implement dynamic sensor 120 comprises an inertialmeasurement unit (IMU), an inclinometer, an accelerometer, a gyroscope,an angular rate sensor, a rotary position sensor, a position sensingcylinder, or combinations thereof. The IMU may include a 3-axisaccelerometer and a 3-axis gyroscope. As shown in FIG. 2, the implementdynamic sensor 120 includes accelerations A_(x), A_(y), and A_(z),respectively representing x-axis, y-axis-, and z-axis accelerationvalues.

The four-bar linkage 112 comprises an implement linkage of length GH, arear side linkage of length FH, a dogbone linkage of length DF, and afront side linkage of length DG. The implement dynamic sensor 120 ispositioned on the dogbone linkage of length DF of the four-bar linkage112. In embodiments, the four-bar linkage comprises a node D, a node F,a node G, a node H. As a non-limiting example, the implement linkage isdisposed between respective positions corresponding to the node G andthe node H. The rear side linkage is disposed between respectivepositions corresponding to the node F and the node H. The dogbonelinkage is disposed between respective positions corresponding to thenode D and the node F, and front side linkage is disposed betweenrespective positions corresponding to the node D and the node G.Further, the node G of the four-bar linkage 112 may be disposed at aposition corresponding to the terminal point of the excavator stick 110through which the excavator stick 110 is coupled to the excavatingimplement 114. Referring to FIG. 5, the four-bar linkage 112 comprises adiagonal length FG between a front end node of the implement linkage oflength GH and a rear end node of the dogbone linkage of length DF.

The excavating implement 114 is configured to curl relative to theexcavator stick 110 to define a plurality of implement curl positions.In embodiments, the excavating linkage assembly 104 may be configured toswing with, or relative to, the machine chassis 102, and the excavatorstick 110 may be configured to curl relative to the excavator boom 108.Further, the machine chassis 102 may be mechanically coupled to aterminal pivot point A of the excavator boom 108. The excavator stick110 may comprise a stick terminal point corresponding to the position ofthe node G of the four-bar linkage 112 and may be mechanically coupledto a terminal pivot point B of the excavator boom 108. Further, theexcavator stick 110 may be mechanically coupled to the excavatingimplement 114 through the stick terminal point. A position of theterminal pivot point B and the node G may be identified prior to, forexample, the iterative process being executed by the architecturecontroller.

Referring to FIG. 3, a boom limb length L_(B) is a limb length of theexcavator boom 108, a boom angle θ_(B) is an angle of the excavator boom108 between the terminal pivot points A and B relative to gravity, astick limb length L_(S) is a limb length of the excavator stick 110, anda stick angle θ_(S) is an angle of the excavator stick 110 between theterminal pivot point B and the node G relative to gravity. One or moredynamic sensors may be disposed on excavator components such as thelimbs of the excavator boom 108 or the excavator stick 110 or on any ofthe linkages of the four-bar linkage 112.

The LDM 124 is configured to generate an LDM distance signal D_(LDM)indicative of a distance between the LDM 124 and the laser reflector 139and an angle of inclination signal θ_(INC) indicative of an anglebetween the LDM 124 and the laser reflector 130. The laser reflector 130is configured to be disposed at a position corresponding to acalibration node on the excavating implement 114. In embodiments, thecalibration node is positioned at a terminal point J at a bucket toothtip of the excavating implement 114. A height H₀ of the LDM 124 from theterminal pivot point A of the excavator boom 108 and a distance D₀ ofthe LDM from a terminal pivot point A of the excavator boom may beidentified or determined prior to, for example, the iterative processbeing executed by the architecture controller.

The control architecture 106 comprises one or more linkage assemblyactuators and an architecture controller programmed to execute aniterative process at successive implement curl positions. Inembodiments, the control architecture comprises a non-transitorycomputer-readable storage medium comprising machine readableinstructions that the architecture controller is programmed to execute.The one or more linkage assembly actuators may facilitate movement ofthe excavating linkage assembly 104. Further, the one or more linkageassembly actuators may comprise a hydraulic cylinder actuator, apneumatic cylinder actuator, an electrical actuator, a mechanicalactuator, or combinations thereof.

The iterative process is illustrated in FIG. 6 through a control scheme200 and steps 202-218. In step 202, the iterative process may start witha first iteration in which m=1. The calibration node may be alignedthrough the excavating linkage assembly 104 to align with the LDM 124 instep 204. The iterative process comprises generating a measured dogboneangle θ_(DF) ^(Measured) of the dogbone linkage from the implementdynamic sensor 120, as illustrated in step 206. The iterative processfurther comprises determining a height Ĥ and a distance {circumflex over(D)} between the calibration node on the excavating implement 114 andthe LDM 124 based on the LDM distance signal D_(LDM) and the angle ofinclination signal θ_(INC), as illustrated in step 208. As shown in step210, the iterative process comprising determining a position of thecalibration node at least partially based on the height Ĥ and thedistance {circumflex over (D)}. Additionally, the iterative processcomprises, as shown in step 212, determining an estimated implementangle θ_(GH) ^(Estimated) of the excavating implement 114 at leastpartially based on the position of the calibration node.

In embodiments, the estimated implement angle θ_(GH) ^(Estimated) of theexcavating implement 114 may be determined at least partially based onthe position of the node G and the position of the terminal pivot pointB. Additionally or alternatively, the estimated implement angle θ_(GH)^(Estimated) of the excavating implement is determined at leastpartially based on a lookup table estimating the based on the measureddogbone angle θ_(DF) ^(Measured). In another embodiment, a position ofthe node D of the four-bar linkage 112 is determined based on themeasured dogbone angle θ_(DF) ^(Measured), or may be otherwiseidentified, and the estimated implement angle θ_(GH) ^(Estimated) of theexcavating implement is determined at least partially based on theposition of the node D and the position of the terminal pivot point B.As a non-limiting example, the estimated implement angle θ_(GH)^(Estimated) of the excavating implement is determined at leastpartially based on a determined internal angle θ_(DGJ) ^(i) that basedon the positions of nodes D and G and the terminal point J. Referring toFIGS. 4-5, a determined external angle θ_(DGJ) ^(e) may be determinedbased on the determined internal angle θ_(DGJ) ^(i) per a followingequation:

θ_(DGJ) ^(e)=360°−θ_(DGJ) ^(i)  (Equation 1)

Further, the determined external angle θ_(DGJ) ^(e) is a sum of theestimated implement angle θ_(GH) ^(Estimated) of the excavatingimplement and a implement angle Ψ that is a constant angle formedbetween surfaces of the excavating implement 114 disposed between theterminal point J and the nodes G and H, such that:

θ_(DGJ) ^(e)=θ_(GH) ^(Estimated)+Ψ  (Equation 2)

(Equation 2)

which is rearranged into a following equation:

θ_(GH) ^(Estimated)=θ_(DGJ) ^(e)−Ψ  (Equation 3)

The iterative process further comprises, as shown in step 214 of FIG. 6,generating a mapping equation comprising linkage angle inputs, unsolvedlinkage length parameters, and unsolved angle offset parameters. Thelinkage angle inputs comprise the measured dogbone angle θ_(DF)^(Measured) and the estimated implement angle θ_(GH) ^(Estimated) at theimplement curl position. The unsolved linkage length parameters comprisethe linkage lengths GH, FH, DF, and DG of the four-bar linkage. Theunsolved angle offset parameters comprise an offset dogbone angle θ_(DF)^(Bias) of the dogbone linkage, and an offset implement angle θ_(GH)^(Bias) of the excavating implement 114.

In embodiments, the mapping equation comprises a following equation,which includes an actual dogbone angle θ_(DF) ^(Actual) and an actualimplement angle θ_(GH) ^(Actual):

$\begin{matrix}{\theta_{GH}^{Actual} = {\frac{{DG} - {{DF}*{\cos \left( {{180{^\circ}} - \theta_{DF}^{Actual}} \right)}}}{FG} + \frac{\begin{matrix}{{DF}^{2} + {DG}^{2} + {GH}^{2} - {2*}} \\{{{DF}*{DG}*\cos \left( {{180{^\circ}} - \theta_{DF}^{Actual}} \right)} - {FH}^{2}}\end{matrix}}{2*{FG}*{GH}}}} & \left( {{Equation}\mspace{14mu} 4} \right)\end{matrix}$

The actual dogbone angle θ_(DF) ^(Actual) is based on the measureddogbone angle θ_(DF) ^(Measured) and the offset dogbone angle θ_(DF)^(Bias) such that:

θ_(DF) ^(Actual)=θ_(DF) ^(Measured)−θ_(DF) ^(Bias)  (Equation 5)

the actual implement angle θ_(GH) ^(Acutal) is based on the estimatedimplement angle θ_(GH) ^(Estimated) and the offset implement angleθ_(GH) ^(Bias) such that:

θ_(GH) ^(Actual)=θ_(GH) ^(Estimated)−θ_(GH) ^(Bias)  (Equation 6)

Further, the mapping equation is based on an implement angle equation,as follows:

$\begin{matrix}{\theta_{GH}^{Actual} = {\frac{{DG}^{2} + {FG}^{2} - {DF}^{2}}{2*{FG}*{DG}} + \frac{{FG}^{2} + {GH}^{2} - {FH}^{2}}{2*{FG}*{GH}}}} & \left( {{Equation}\mspace{14mu} 7} \right)\end{matrix}$

The implement angle equation is based on an implement angle summationequation, as follows:

θ_(GH) ^(Actual)=θ_(FGD)+θ_(HGF)  (Equation 8)

In Equation 8, θ_(HGF) is an angle between nodes H, G, and F, andθ_(FGD) is an angle between nodes F, G, and D. Further, θ_(HGF) andθ_(FGD) are based on a following pair of equations:

$\begin{matrix}{{\theta_{FGD} = \frac{{DG}^{2} + {FG}^{2} - {DF}^{2}}{2*{FG}*{DG}}}{and}{\theta_{HGF} = \frac{{FG}^{2} + {GH}^{2} - {FH}^{2}}{2*{FG}*{DH}}}} & \left( {{Equations}\mspace{14mu} 9\text{-}10} \right)\end{matrix}$

The mapping equation is further based on a substitution of a FG² term inthe implement angle equation with a diagonal length squared equation,which follows:

FG ² =DF ² +DG ²−2*DF*DG*cos(180°−θ_(DF) ^(Actual))  (Equation 11)

Further, the diagonal length squared equation of Equation 11 is based ona diagonal length equation, as follows:

FG=√{square root over (DF ² +DG ²−2*DF*DG*cos(180°−θ_(DF)^(Actual)))}  (Equation 12)

In embodiments, the mapping equation maps a waveform as, for example, agraphical empirical chart or display, the waveform comprising linear andnon-linear regions at least partially based on one or more linkagelengths.

The architecture controller is further programmed to repeat theiterative process for successive implement curl positions to generate aset of m mapping equations, wherein the set of m mapping equationscomprises n unsolved linkage length and unsolved angle offsetparameters, and the iterative process is repeated until m>n. Forexample, as shown in step 216 of FIG. 6, if m>n is not true, then theiterative process continues to step 218 and the next iteration of m torepeat through steps 204-216. If, in step 216, m>n is true, the controlscheme 200 continues on to step 220. In embodiments, the iterativeprocess is repeated until m passes a threshold greater than n. As anon-limiting example, n may be equal to 6 and the threshold may be 17such that m is equal to 18 to generate a set of 18 mapping equationscomprising 6 unsolved linkage length and unsolved angle offsetparameters.

As shown in step 220 of FIG. 6, the architecture controller is furtherprogrammed to solve the generated set of m mapping equations comprisingthe n unsolved parameters to determine the linkage lengths GH, FH, DF,and DG of the four-bar linkage, the offset dogbone angle θ_(DF) ^(Bias)of the dogbone linkage, and the offset implement angle θ_(GH) ^(Bias) ofthe excavating implement 114. Further, as shown in step 222 of FIG. 6,the architecture controller is programmed to operate the excavator 100using the n solved parameters of linkage lengths GH, FH, DF, and DG, theoffset dogbone angle θ_(DF) ^(Bias), and the offset implement angleθ_(GH) ^(Bias).

It is contemplated that the embodiments of the present disclosure mayassist to permit a speedy and more cost efficient method of determininglinkage lengths, sensor offsets of sensors on excavator linkages, andoffsets of angular estimations of excavator linkages in a manner thatminimizes a risk of human error with such value determinations. Further,the controller of the excavator or other control technologies areimproved such that the processing systems are improved and optimizedwith respect to speed, efficiency, and output.

A signal may be “generated” by direct or indirect calculation ormeasurement, with or without the aid of a sensor.

For the purposes of describing and defining the present invention, it isnoted that reference herein to a variable being a “function” of aparameter or another variable is not intended to denote that thevariable is exclusively a function of the listed parameter or variable.Rather, reference herein to a variable that is a “function” of a listedparameter is intended to be open ended such that the variable may be afunction of a single parameter or a plurality of parameters.

It is also noted that recitations herein of “at least one” component,element, etc., should not be used to create an inference that thealternative use of the articles “a” or “an” should be limited to asingle component, element, etc.

It is noted that recitations herein of a component of the presentdisclosure being “configured” or “programmed” in a particular way, toembody a particular property, or to function in a particular manner, arestructural recitations, as opposed to recitations of intended use. Morespecifically, the references herein to the manner in which a componentis “configured” or “programmed” denotes an existing physical conditionof the component and, as such, is to be taken as a definite recitationof the structural characteristics of the component.

It is noted that terms like “preferably,” “commonly,” and “typically,”when utilized herein, are not utilized to limit the scope of the claimedinvention or to imply that certain features are critical, essential, oreven important to the structure or function of the claimed invention.Rather, these terms are merely intended to identify particular aspectsof an embodiment of the present disclosure or to emphasize alternativeor additional features that may or may not be utilized in a particularembodiment of the present disclosure.

For the purposes of describing and defining the present invention it isnoted that the terms “substantially” and “approximately” are utilizedherein to represent the inherent degree of uncertainty that may beattributed to any quantitative comparison, value, measurement, or otherrepresentation. The terms “substantially” and “approximately” are alsoutilized herein to represent the degree by which a quantitativerepresentation may vary from a stated reference without resulting in achange in the basic function of the subject matter at issue.

Having described the subject matter of the present disclosure in detailand by reference to specific embodiments thereof, it is noted that thevarious details disclosed herein should not be taken to imply that thesedetails relate to elements that are essential components of the variousembodiments described herein, even in cases where a particular elementis illustrated in each of the drawings that accompany the presentdescription. Further, it will be apparent that modifications andvariations are possible without departing from the scope of the presentdisclosure, including, but not limited to, embodiments defined in theappended claims. More specifically, although some aspects of the presentdisclosure are identified herein as preferred or particularlyadvantageous, it is contemplated that the present disclosure is notnecessarily limited to these aspects.

It is noted that one or more of the following claims utilize the term“wherein” as a transitional phrase. For the purposes of defining thepresent invention, it is noted that this term is introduced in theclaims as an open-ended transitional phrase that is used to introduce arecitation of a series of characteristics of the structure and should beinterpreted in like manner as the more commonly used open-ended preambleterm “comprising.”

What is claimed is:
 1. An excavator calibration framework comprising anexcavator, a laser distance meter (LDM), and a laser reflector, wherein:the excavator comprises a machine chassis, an excavating linkageassembly, an implement dynamic sensor, an excavating implement, and anarchitecture controller; the excavating linkage assembly comprises anexcavator boom, an excavator stick, and a four-bar linkage; theexcavating implement and the excavator stick are mechanically coupledthrough the four-bar linkage comprising an implement linkage of lengthGH, a rear side linkage of length FH, a dogbone linkage of length DF,and a front side linkage of length DG; the implement dynamic sensor ispositioned on the dogbone linkage of the four-bar linkage; theexcavating implement is configured to curl relative to the excavatorstick to define a plurality of implement curl positions; the LDM isconfigured to generate an LDM distance signal D_(LDM) indicative of adistance between the LDM and the laser reflector and an angle ofinclination signal θ_(INC) indicative of an angle between the LDM andthe laser reflector; the laser reflector is configured to be disposed ata position corresponding to a calibration node on the excavatingimplement; the architecture controller is programmed to generate amapping equation comprising linkage angle inputs, unsolved linkagelength parameters, and unsolved angle offset parameters, wherein thelinkage angle inputs comprise a measured dogbone angle θ_(DF)^(Measured) and an estimated implement angle θ_(GH) ^(Estimated) at animplement curl position, the unsolved linkage length parameters comprisethe linkage lengths GH, FH, DF, and DG of the four-bar linkage, and theunsolved angle offset parameters comprise an offset implement angleθ_(GH) ^(Bias) of the excavating implement; for successive implementcurl positions, generate a set of m mapping equations, wherein the setof m mapping equations comprises n unsolved linkage length and unsolvedangle offset parameters, and the iterative process is repeated untilm>n, solve the generated set of m mapping equations comprising the nunsolved parameters to determine the linkage lengths GH, FH, DF, and DGof the four-bar linkage and the offset implement angle θ_(GH) ^(Bias) ofthe excavating implement, and operate the excavator using the linkagelengths GH, FH, DF, and DG, and the offset implement angle θ_(GH)^(Bias).
 2. An excavator calibration framework as claimed in claim 1,wherein: the four-bar linkage comprises a node D, a node F, a node G, anode H; the implement linkage is disposed between respective positionscorresponding to the node G and the node H; the rear side linkage isdisposed between respective positions corresponding to the node F andthe node H; the dogbone linkage is disposed between respective positionscorresponding to the node D and the node F; and the front side linkageis disposed between respective positions corresponding to the node D andthe node G.
 3. An excavator calibration framework as claimed in claim 2,wherein the node G of the four-bar linkage is disposed at a positioncorresponding to a terminal point of the excavator stick through whichthe excavator stick is coupled to the excavating implement.
 4. Anexcavator calibration framework as claimed in claim 1, wherein theiterative process is repeated until m passes a threshold greater than n.5. An excavator calibration framework as claimed in claim 4, wherein nis equal to 6 and the threshold is 17 such that m is equal to 18 togenerate a set of 18 mapping equations comprising 6 unsolved linkagelength and unsolved angle offset parameters.
 6. An excavator calibrationframework as claimed in claim 1, wherein the laser reflector is on apole or secured directly to the excavating implement.
 7. An excavatorcalibration framework as claimed in claim 1, wherein the calibrationnode is positioned at a terminal point J at a bucket tooth tip of theexcavating implement.
 8. An excavator calibration framework as claimedin claim 1, wherein the machine chassis is mechanically coupled to aterminal pivot point A of the excavator boom.
 9. An excavatorcalibration framework as claimed in claim 1, wherein the excavator stickcomprises a stick terminal point corresponding to the position of a nodeG of the four-bar linkage and is mechanically coupled to a terminalpivot point B of the excavator boom; and the excavator stick ismechanically coupled to the excavating implement through the stickterminal point.
 10. An excavator calibration framework as claimed inclaim 9, wherein a position of the terminal pivot point B and the node Gare identified.
 11. An excavator calibration framework as claimed inclaim 10, wherein the estimated implement angle θ_(GH) ^(Estimated) ofthe excavating implement is determined at least partially based on theposition of the node G and the position of the terminal pivot point B.12. An excavator calibration framework as claimed in claim 9, wherein:the four-bar linkage comprises a node D, a node F, a node G, a node H;the calibration node is positioned at a terminal point J at a headingtooth tip of the excavating implement; a position of the terminal pivotpoint B is identified; a position of the node D of the four-bar linkageis determined based on the measured dogbone angle θ_(DF) ^(Measured);and the estimated implement angle θ_(GH) ^(Estimated) of the excavatingimplement is determined at least partially based on the position of thenode D and the position of the terminal pivot point B.
 13. An excavatorcalibration framework as claimed in claim 12, wherein the estimatedimplement angle θ_(GH) ^(Estimated) of the excavating implement isdetermined at least partially based on: a determined internal angleθ_(DGJ) ^(i) based on the positions of nodes D and G and the terminalpoint J such that a determined external angle θ_(DGJ) ^(e)=360°−θ_(DGJ)^(i).
 14. An excavator calibration framework as claimed in claim 13,wherein the determined external angle θ_(DGJ) ^(e) is a sum of theestimated implement angle θ_(GH) ^(Estimated) of the excavatingimplement and a implement angle Ψ that is a constant angle formedbetween the surfaces of the excavating implement disposed between theterminal point J and the nodes G and H, such that:θ_(GH) ^(Estimated)=θ_(DGJ) ^(e)−Ψ.
 15. An excavator calibrationframework as claimed in claim 1, wherein: the four-bar linkage comprisesa diagonal length FG between a front end node of the implement linkageof length GH and a rear end node of the dogbone linkage of length DF;and the mapping equation comprises a following equation, including anactual dogbone angle θ_(DF) ^(Actual) and an actual implement angleθ_(GH) ^(Actual):$\theta_{GH}^{Actual} = {\frac{{DG} - {{DF}*{\cos \left( {{180{^\circ}} - \theta_{DF}^{Actual}} \right)}}}{FG} + {\frac{\begin{matrix}{{DF}^{2} + {DG}^{2} + {GH}^{2} - {2*}} \\{{{DF}*{DG}*\cos \left( {{180{^\circ}} - \theta_{DF}^{Actual}} \right)} - {FH}^{2}}\end{matrix}}{2*{FG}*{GH}}.}}$
 16. An excavator calibration framework asclaimed in claim 15, wherein: the actual dogbone angle θ_(DF) ^(Actual)is based on the measured dogbone angle θ_(DF) ^(Measured) and an offsetdogbone angle θ_(DF) ^(Bias) such that:θ_(DF) ^(Actual)=θ_(DF) ^(Measured)−θ_(DF) ^(Bias); and the actualimplement angle θ_(GH) ^(Actual) is based on the estimated implementangle θ_(GH) ^(Estimated) and the offset implement angle θ_(GH) ^(Bias)such that:θ_(GH) ^(Actual)=θ_(GH) ^(Estimated)−θ_(GH) ^(Bias).
 17. An excavatorcalibration framework as claimed in claim 15, wherein the mappingequation is based on an implement angle equation, as follows:$\theta_{GH}^{Actual} = {\frac{{DG}^{2} + {FG}^{2} - {DF}^{2}}{2*{FG}*{DG}} + \frac{{FG}^{2} + {GH}^{2} - {FH}^{2}}{2*{FG}*{GH}}}$and a substitution of a FG² term in the implement angle equation with adiagonal length squared equation, as follows:FG ² =DF ² +DG ²−2*DF*DG*cos(180°−θ_(DF) ^(Actual)).
 18. An excavatorcalibration framework as claimed in claim 17, wherein the diagonallength squared equation is based on a diagonal length equation, asfollows:FG=√{square root over (DF ² +DG ²−2*DF*DG*cos(180°−θ_(DF) ^(Actual)).)}19. An excavator calibration framework as claimed in claim 17, whereinthe implement angle equation is based on an implement angle summationequation, as follows:θ_(GH) ^(Actual)=θ_(FGD)+θ_(HGF).
 20. An excavator, wherein: theexcavator comprises a machine chassis, an excavating linkage assembly,an implement dynamic sensor, an excavating implement, and anarchitecture controller; the excavating linkage assembly comprises anexcavator boom, an excavator stick, and a four-bar linkage; theexcavating implement and the excavator stick are mechanically coupledthrough the four-bar linkage comprising an implement linkage of lengthGH, a rear side linkage of length FH, a dogbone linkage of length DF,and a front side linkage of length DG; the implement dynamic sensor ispositioned on the dogbone linkage of the four-bar linkage; theexcavating implement is configured to curl relative to the excavatorstick to define a plurality of implement curl positions; thearchitecture controller is programmed to generate a measured dogboneangle θ_(DF) ^(Measured) of the dogbone linkage from the implementdynamic sensor, generate a mapping equation comprising linkage angleinputs, unsolved linkage length parameters, and unsolved angle offsetparameters, wherein the linkage angle inputs comprise the measureddogbone angle θ_(DF) ^(Measured) and an estimated implement angle θ_(GH)^(Estimated) at an implement curl position, the unsolved linkage lengthparameters comprise the linkage lengths GH, FH, DF, and DG of thefour-bar linkage, and the unsolved angle offset parameters comprise anoffset dogbone angle θ_(DF) ^(Bias) of the dogbone linkage, andan-offset implement angle θ_(GH) ^(Bias) of the excavating implement;for successive implement curl positions, generate a set of m mappingequations, wherein the set of m mapping equations comprises n unsolvedlinkage length and unsolved angle offset parameters, and the iterativeprocess is repeated until m>n, solve the generated set of m mappingequations comprising the n unsolved parameters to determine the linkagelengths GH, FH, DF, and DG of the four-bar linkage, the offset dogboneangle θ_(DF) ^(Bias) of the dogbone linkage, and the offset implementangle θ_(GH) ^(Bias) of the excavating implement, and operate theexcavator using the linkage lengths GH, FH, DF, and DG, the offsetdogbone angle θ_(DF) ^(Bias), and the offset implement angle θ_(GH)^(Bias).